LONDON (Reuters) - Britain should move quickly to keep investment flowing and preserve the City of London's dominance in financial services after last month's vote to leave the European Union, the head of London's financial district said on Wednesday.

Jeffrey Mountevans, Lord Mayor of London, said Britain must protect access to the EU's single market by maintaining so-called passporting rights after it leaves the bloc.

Banks, asset managers and clearing houses in Britain currently serve customers across the EU under a passport system that give access to the single market if they comply with all the bloc's regulations.

Britain will have to negotiate new trading terms with the EU but it is unclear if any passporting rights will be maintained. Without them, banks in Britain could be cut off from a large chunk of the European market.

"It is in all our interests to protect access to the single market, protect the UK's flexible labor market, protect the City's passporting rights," Mountevans will say later on Wednesday in a speech made available to the media.

"We all hope that the UK government will act swiftly to ensure continued investment in this country – and continued competitiveness for our international firms."

London offers by far the deepest pool of capital in the time zone between Asia and the United States but also lawyers and accountants, luxury property and shopping, quality private education and a wider cultural renaissance unmatched in Europe.

Many fear the Brexit vote, and the turmoil it has unleashed, puts London's prosperity under threat.

Brussels insists that to maintain passporting rights, Britain would have to continue allowing EU citizens to live and work in the UK, an anathema to many of the British politicians and voters who backed Brexit.

The City of London, a municipal authority that administers the capital's "square mile" financial district, had campaigned to stay in the EU.

Mountevans also pointed to potential knock on effects from Brexit on sectors that support financial services, with London the headquarters for four of the 10 biggest global law firms.

France, Germany and the Netherlands hope banks will move to their financial centers in order to remain inside the single market.

Britain will begin formulating the new trading terms it seeks once a new UK prime minister has been chosen in September and Mountevans said the financial industry must have a say.

"We need early and extensive consultation on the way forward – drawing on the expertise of UK financial, professional and business services," he said.